Adding 1d4 damage to the weapon would be a similar effect
Challege with the Question
The challenge with this question is that, the power a +1 weapon in terms of the average additional damage varies depending on a large number of factors:
- What type of weapon is it? (Higher damage weapons get more benefit from +1 to hit)
- What is the characters attack bonus? (a higher attack bonus makes the +1 to hit less valuable)
- Are you attacking with advantage / disadvantage? (More useful if you have disadvantage and less useful with advantage)
- Are you dealing sneak attack damage? Are you an assassin with auto-crit possibility? (Both of these make the value of a +1 to hit higher)
Value of a +1 Weapon
Given the above, I am going to make a series of assumptions in my answer, let me know in the comments if you think these are wrong / unreasonable:
- You are a level 4 rogue
- Your Dex modifier is +4 and proficiency bonus if +2
- You are using a rapier as your weapon dealing 1d8 + 4 damage on a hit
- You are getting sneak attack on 50% of your attacks
- You are fighting enemies with an average AC of 13
- You have neither advantage or disadvantage
Based on this:
The average damage that you deal with a normal rapier will be 8.8
The average damage that you will deal with a +1 rapier will be 10.15
So in terms of damage output, the +1 weapon increases your damage output by 1.35 per attack.
Comparing with Other Effects
1d4 to Every Roll
If instead of a +1 weapon you added 1d4 of damage to every roll, this would increase the average damage by 1.875 so this would be marginally stronger than a +1 weapon. If you picked a damage type (e.g. Fire) which is commonly resisted then this would be a reasonably comparable weapon
Higher damage dice
If you are using a higher damage dice, this quickly becomes much stronger. Even a 1d6 means that the damage is 2.625 higher than the base weapon which is double the benefit of a +1 weapon. So if using a higher damage dice, I would say you should limit the effect to a fixed number of uses per day. The higher the dice, the fewer uses it should have.
Other spell effect
I am not going to detail all the spell effects and their relative benefits, but for any proposed effect I would recommend looking at the expected impact on damage (or the battle in general) and seeing how this compares to the impact of the +1 weapon.
You can also look at other magical items which produce spell effects and see the rarity of these items. This should give you a steer on whether or not the effect is overpowered.