Perhaps the main reason I prefer to start with Ivy, besides the good damage racking opportunities, is to make sure Charizard doesn't come out until high percents. Getting tech-chased from 0% til whenever is a great way to ruin your momentum.
Starting with Squirtle often leads to this, at least for me.
--Squirtle goes out. Life's great. Snake's up to high damage.
GOOD
----Squirtle gets the KO and switches to Ivy during respawn. Ivy's at high %.
MEH
------Ivy gets KO'd quickly and a 0% Zard comes out.
BAD
OR
----Squirtle switches to Ivy to get KO. Ivy switches to Charizard comes out at high %
GOOD
------Charizard gets KO'd before Squirtle is fully rested.
BAD
OR
------Charizard manages to stall long enough for Squirtle to recover.
GOOD
Starting with Ivysaur often follows this pattern.
--Ivysaur racks up damage. Life's alright, a little dangerous.
MEH
----Ivysaur gets the KO. (WTF?) Charizard comes out at high %.
GOOD
------Charizard's not techchase bait. Gets KO'd. Fresh Squirtle comes out.
GOOD
OR
----Ivysaur switches to Charizard to get the KO. Charizard is at high %.
GOOD
------Charizard's again not techchase bait. Gets KO'd. Fresh Squirtle comes out.
GOOD
Without going into a long and complicated details...
The Squirtle lead situation has the potential to lead into a 0% Charizard two or three times before the match is over. This is because by leading with Squirtle, theres alot more room to get KO'd, especially when switching to Ivy, before Charizard comes out. This pattern places high reliance on Squirtle, the best pokemon, at the risk of putting yourself in a bad position.
The Ivysaur lead situation only has one, or at worst, two points at which a miscalculation could lead to a 0% Charizard. This is because leading with Ivy bypasses the risk from the first stock, and puts the player in a better position to juggle their pokemon and make sure Charizard comes out only when damage is high. This strategy takes some emphasis off of Squirtle and places it on Ivy, the weaker of the two, but with the benefit of avoiding potentially bad situations.
In short...
If you want to maximize your time with the best pokemon for the job, start with Squirtle. Just be aware that with the problem of Fatigue an 0% Charizard, that momentum gained in the first stock is going to be considerably more difficult to keep.
If you want to stay safe in the late game, stick with Ivysaur. It's more difficult to gain momentum with her, but if you can manage the first stock, you shouldn't have to worry too much from there. 0% Charizard and Fatigue are much more easily averted.
Really, it just depends on what situation you want to put yourself in. Getting in a strong lead is important, of course. Squirtle, despite the danger of late game trouble, is the better option. Ivysaur, I think though, is the safer one.