Basic Evocation Wizards are now the equivalent of Tier 3 at lower levels.
Basic Champion Fighters are now the equivalent of Tier 3 at lower levels.
The Usefulness of Tiers will have to change for 5e, as tiers 1, 5, and 6 at this time don't exist, and likely won't exist as the overall power of 5e is much flatter.
For overall power however, it's going to really depend on level.
Thanks to the work by @Waxeagle we can see how power via damage shifts over level.
Basically at level 11, the Fighter is doing more damage than the evocation wizard who is focused solely on damage. However, by level 17, both the cleric and the Wizard have enough spell slots, to out perform the Fighter and Rogue. In addition, level 9 spells are by their nature "game changers". It should be noted that at level 20, with the third extra attack, the fighter shoots up in power as well, though not enough to out perform spells such as meteor storm, the nuclear weapon of D&D. One caveate to the current graph is that not all levels are shown, only the level when the "adventure tier" changes. For example, not shown on the graph is level 10, where the fighter still only has one extra attack, the wizard and cleric are doing about the same amount as the fighter.
So while it is still the case at the highest levels that magic is more powerful than the mundane, up until the epic tier, this problem does not really present itself.
This obviously doesn't take into account the non-damaging effects of spells, such as haste, or invisibility, or flying, etc. However, with the new concentration mechanic, these spells are situational and can not be easily piled on top of each other as they could in 3rd edition, to create a quadratic power curve.
Relevant data for the chart:
The above chart is based on the various classes an unlimited number of enemies with the following defenses, and no assumption is made about the HP of the monster, so damage is "unbounded" in the terms of the spreadsheet:
Dex Save 2
Con Save 2
However, If I change the defences of the monsters to something less reasonable in the game, such as giving a Dex and Con save of 5 and an AC of 10, we see the fighter keeping up with the wizard and again surpassing it at level 20.
You can compare these 5e graphs, to this 3.5 graph and notice how the fighter is at the bottom of the graph and stays very linear, while the wizard has a slight a quadradic curve in power gains.
(Graph taken from here)
Old Long Answer about Tiers:
First, the assertion that a Wizard might be tier 1:
Tier 1: Capable of doing absolutely everything, often better than
classes that specialize in that thing. Often capable of solving
encounters with a single mechanical ability and little thought from
the player. Has world changing powers at high levels. These guys, if
played well, can break a campaign and can be very hard to challenge
without extreme DM fiat, especially if Tier 3s and below are in the
It's pretty clear that currently, the Evocation Wizard can not do absolutely everything. Because of the concentration mechanic, the Wizard can really only do one cool thing at a time. You can't fly and be invisible at the same time without another magic item or wizard casting those spells on you, for example. Secondly, while some spells can duplicate other class abilities, such as "knock", those spells are only situationally better, and come at a high resource spot (limited spell slots) that other classes lack. So the Wizard is no longer a tier 1 class.
Instead, I would say that Tier 3 fits the Evocation Wizard.
Tier 3: Capable of doing one thing quite well, while still being
useful when that one thing is inappropriate, or capable of doing all
things, but not as well as classes that specialize in that area.
Occasionally has a mechanical ability that can solve an encounter, but
this is relatively rare and easy to deal with. Challenging such a
character takes some thought from the DM, but isn't too difficult.
Will outshine any Tier 5s in the party much of the time.
The bolded part is why I believe a Wizard is Tier 3. A wizard can, if picked the right spells, do anything another class can do (with some exceptions), but it can't do those things as well as the class that specializes in that thing. An invisible wizard is hidden, but can't sneak. A wizard with damage spells, can't kill, a single high hitpoint target as well as a fighter can. A Rogue will have better skill abilities when it specializes in those skills than a wizard can ever get.
Next the assertion that a fighter is tier 5.
Tier 5 is defined by:
Tier 5: Capable of doing only one thing, and not necessarily all that
well, or so unfocused that they have trouble mastering anything, and
in many types of encounters the character cannot contribute. In some
cases, can do one thing very well, but that one thing is very often
not needed. Has trouble shining in any encounter unless the rest of
the party is weak in that situation and the encounter matches their
strengths. DMs may have to work to avoid the player feeling that their
character is worthless unless the entire party is Tier 4 and below.
Characters in this tier will often feel like one trick ponies if they
do well, or just feel like they have no tricks at all if they build
the class poorly.
No class is good at only one thing. Because of the Background system, all classes and characters are able to focus on skills that are outside of their class. So while you can make a fighter that is only good at fighting, and can't do anything during exploration or social interactions, it's also more likely to build a fighter that is good at fighting and leading people. Or good at fighting and using certain tools. Because of bounded Accuracy, all characters are decent at whatever skill they are proficient in. The champion fighter is best built for two handed heavy weapons, but they can also be a good archer, or duelist. Fighters excel in combat and at higher levels, can move across the battle field, hitting multiple creatures in one turn in the same way that a wizard might target more than one creature with a spell. They are also able to survive situations that others would not without a cleric. So I don't think they can be called Tier 5.
Champion fighters are however tier 3, because they are
Capable of doing one thing quite well, while still being useful when that one thing is inappropriate.
Fighters do combat really well, they survive well and can kill well. However sometimes a situation will be called where there is no combat. Fighters can excel at jumping across chasms, or climbing/swimming out of tough spots more so than wizards and clerics. With Background again, they can also call upon their traits. In the starter set for example, the Fighter is a folk hero, who is able to rally others to their cause.
However, the tier system as a whole is a bad way to judge D&D 5e classes. The power level of the entire system has been made "more flat", and there will need to be better definitions of how to compare classes.