The differences mostly have to do with tournament administration. Maybe there is argument for minor game influences, but here we care more about the chips than strategery

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T25 I believe became common because that was the WSOP main event structure at the time of the "poker boom" 20 years ago. 10K starting stacks, 25-50 starting blinds. This was the structure at the very first WSOP in fact, where they just played a one table cash game and voted on the winner.
Starting stack construction
For simplicity, let's consider starting stacks of 200 BB assuming blinds start at 1-2 times the base chip.
Base | First Level | Starting Stack | Denominations | Tight Quantity* | Loose Quantity* |
T1 | 1-2 | 400 | 1/5/25/100 | 10/8/6/2 (26 chips) | 15/12/9/1 (37 Chips) |
T5 | 5-10 | 2000 | 5/25/100/500 | 10/6/8/2 (26 chips) | 15/9/12/1 (37 Chips) |
T25 | 25-50 | 10,000 | 25/100/500/1K | 8/8/2/8 (26 chips)** | 12/12/5/6 (35 Chips) |
T100 | 100-200 | 40,000 | 100/500/1K/5K | 10/2/8/6 (26 chips)** | 15/3/12/5 (35 Chips) |
T500 | 500-1000 | 200,000 | 500/1K/5K/25K | 4/8/8/6 (26 chips) | 6/12/12/5 (35 Chips) |
*Tight quantity means all lower chips in the set should make 2 of the next value chip until the starting stack amount is reached. Loose Quantity means all lower chips in the starting stack should be able to make 3 of the next value chip until the starting stack amount is reached.
**More commonly these breakdowns have 4 * T500 in their stacks instead instead of 2, and one fewer T1000, which would call for a net increase of one chip.
Some bases require more chips in the tight quantity, some require more in the loose quantity. The T500 is the only base that's the most "efficent" in terms of fewest starting chips in both worlds.
Color Ups
If you consider the denominations you can list out a progression of multiples for each base.
T1 - 5x/5x/4x
T5 - 5x/4x/5x
T25 - 4x/5x/2x
T100 - 5x/2x/5x
T500 - 2x/5x/5x
The multiples also influence where the natural color ups are. Assuming you follow a progression of levels that play 2-4, 3-6, 4-8, 6-12, 8-16 times each chip in play, going back to start every time you can reach 2-4 times the next chip in play, it takes 5 levels to do a 5x color up, 4 levels to do a 4x color up, and 2 levels to do a 2x color up. The exception being at the start of the tournament, you may add possibly three levels of 1-1, 1-2, and 1-3 times the base chip before playing the 2-4 level.
So with Base T1, T5, and T100 you will play 7-8 levels before a color up.
With Base T25 you would play 6-7 levels
With Base T500 you would play 4-5 levels.
Also of note, the formats that start on 5x jump remove the most chips in the first color up. The T500 base has the simplest color up at the start and removes the fewest chips from play.
I don't know if any of this is significant, but these two things are the only real obvious differences in the bases to me. A lot of it is personal preference and what fits your desired structure best.