**There is no RAW answer here.** 

By RAW both group and individual checks are allowed for this. It is **entirely up to the DM.**

That being said, here is what I would do:

**Use group checks for overland movement**

When moving on the "world map", if players are trying to be stealthy (keep in mind this means moving at a slower overland pace than normal) to avoid encounters or to be able to ambush things they do encounter, I would use the group check. This makes a lot of sense, as overland movement is a lot of averaging things over time. It is easier for more skilled members to cover for the mistakes of less skilled ones in these situation (the rogue telling the paladin where to step to avoid crunching branches, getting his armor stuck on things that make noise, etc).

This also allows for army scale ambushes, which are real things. It makes little since that an army just auto fails ambush attempts as inevitably someone would roll a 1 in a group of hundreds.

**Use individual checks for dungeons**

This is the rogues turn to shine. When in a dungeon to scout ahead or trying to sneak past a guard, etc, each PC that attempts it has to make a check. Things on this scale it makes way more sense for a single bad roll to give you away. This allows the high stealth character to be really happy with their choice to invest in being stealthy. It also makes it realistic. Yes a Paladin in full plate is very likely to give away your position. This allows the rogue to sneak ahead scout the area so the party knows what they are up against, without letting the whole party just bypass all the challenges with a much easier group check. 

If the whole party does need to get by without fighting and they don't like their odds with individual checks, they will need to get creative. Have the paladin remove their armor. Cast invisibility on the least stealthy people, granting them advantage. Invest in boots and cloak of elven kind. Use slight of hand to create a distraction, tossing a rock from around a corner down the wrong hallway (an arcane trickster with mage hand can do a lot of creative distractions), the guards going to check the noise the group getting advantage to sneak by. Use suggestion, dominate, deception, or other non-stealth ways to get passed the guard. These up close and personal situations require creative game-play or sheer luck.