If you had 2 bikes, same geometry, same suspension design, same frame material but one had 100mm travel and the other 150mm travel, would they feel the same when pedalling?

Not quite. The one with more travel will also have more sag, and sag will change the actual geo (remember geometry numbers are usually reported without sag). Also they would feel fairly different while riding, longer travel requiring a bit better form while pedaling.

Lets assume that the frame was designed to take that range of fork lengths. At 100mm it will feel very responsive, climb well but be twitchy on the downhill stuff and the front end is likely to fold under.
At 150mm it will have slower steering, be more stable downhill but more likely to lift the front whilst climbing.
The difference in fork length will change the head angle. Downhill bikes run slacker head angles, around 65 degrees and XC bikes are closer to 70 degrees.
When pedalling the longer fork will have more sag and I would imagine the pedal bob will be far more pronounced especially when climbing.
There are loads of other variables but try to make sure that your frame is designed for the fork you intend to fit. Most adjustable forks have a range of 30mm so I would imagine that 50mm is too much.

Oxymoron.

They cannot have the same geometry.

Depends on the terrain as both are designed for off road riding.

If it was mounted on a treadmill however………. 8)

Oxymoron.

They cannot have the same geometry.

Sure they can, in theory, you could make a bike with 100mm travel but the geometry of a 150mm bike it’s just that nobody wants to, so nobody has done it…

TBH though It’s all a bit too hyperthetical really, I suppose the simple answer is that of course they would feel different the suspension reaction to rider input and terrain will always vary with more or less travel available…

Real world wise you’d tend to buy a bike where the geometry/suspension fits your requirements eg; You won’t buy a DH bike when you need an XC whippet, and you won’t buy a 9″ DH bike when you need a trail bike… Or you might, I dunno it’s your choice…

if you really want to make a 150mm bike behave like a 100mm one, take about 50mm off the travel…