Lens Design - flat or dome lens?

So I've got this P60 Boker light that I purchased in ~2004. Carried it quite a bit but had to box it up because reasons. One of those reasons being, the heat from the P60 lamp cause the curved plastic lens to crack.
I recently pulled it out of a box, removed the cracked lens and took a caliper to measure the head opening. Got on ebay and ordered 2 glass watch lenses. One is flat. One is domed. Is there any noticeable difference in output depending on the lens shape?
Also, anyone recomend an adhesive/sealant to secure the lens in place?

I don't see why the output should change when using a flat-lens compared to a domed one. However, using a different lens will most probably affect how the light is focused, resulting perhaps in a different perceived brightness, as the beam might become more floody or throwy. But this all depends on the reflector and LED used as well as the lens/glass.

In watchmaking we often use a two-component adhesive to secure watch-glasses and indices on dials. They work very quickly once mixed, and once dry, are almost impossible to remove again (from your fingers too...). I do however not know how this kind of glue stands up to high temperatures, so I cannot help you with that. My guess is it should be fine?

Right. I guess I should have worded it more properly. I understand that the output will be the same but as you say the perceived output will differ depending on shape of beam.
Most lenses i see are flat, but there is the occasional curved lens.
I'm looking for a less permanent adhesive. I obviously would like to be secure but i want something that, should the glass break, can be removed for a new lens without hacking and destroying the housing.

I would think a rubber gasket or a big o-ring. What was there originally? I think the curved lense would make it more of a focused flood and a flat one would give you a normal hot spot and some spill. I never owned a surefire so I'm not sure. Maybe others will chime in and say.

Its not exactly a Surefire. Its a Boker but designed with a Surefire P60 bulb.
It had a curved plastic lens. The lens rested on a lip inside the head. It was sealed with an O-ring but secured in place with some sort of adhesive. My plan was to simply run a bead of sealant along that lip and seat the lens on it and allow the sealant to seal and secure the lens. I'm sure I'm over complicating it. I reckon i could just use some clear rtv and call it good.

Back in the day Vital Gear lights had a curved lens to attempt to blend the hot spot of a P60 a little wider while still proving as much throw.
There's a subtle difference but not like it's one of those "holy cow what a difference" things.