One shouldn't lose sleep in comparing VTI to VTSAX, both are ideal for buy & hold, but there are a few advantages.
Allowing fractional shares is down to the brokerage. Many offer fractional share purchases of VTI (strangely, the one outlier is at Vanguard, weird). In terms of 'auto-investing', I'm guessing you are referring to fixed contributions (ex. making a purchase once a month) opposed to auto re-investment of dividends (which is just a setting at your brokerage, so when you get a dividend, you can configure to automatically re-invest and you'll be awarded fractions of share). So if you purchase VTI instead of auto investing 1k a month on the 15th of VTSAX, you'll need to pop into your brokerage account and make a 1k purchase.
Mutual funds (VTSAX) are nice and easy as you just enter a purchase amount and your purchase price is whatever the end of day price is. The ETF (VTI) is whatever the price is at the moment in the trading day, but no real slippage as the fund is so heavily traded. So if you think the market if overreacting to something mid-day and may come to their senses in an hour or so, you might be able to purchase VTI cheaper than what VTSAX settles at the end of the day. Lastly, if you have your account at Vanguard, you can also convert VTSAX to VTI automatically without a taxable event (and your purchase acquisition history carries over).
The main difference is if you are paying
ANY fee to purchase VTSAX. It's free to purchase at Vanguard, JPMorgan, etc, but at Interactive Brokers, there is a fee. If there is a fee to purchase at your brokerage, FULL STOP, you should be purchasing the ETF equivalent (VTI).
The expense ratio for VTI is less (a WHOLE 1 BPS, insignificant, but STILL less). But if the buyer doesn't have 3k (use to be 10k) for VTSAX, VTI is an easier entry.
VTI: 0.03%
VTSAX: 0.04% (min initial investment 3k)
VTSMX: 0.14% (no min investment / same as VTSAX)
But the best part of VTI vs. VTSAX, PORTABILITY! Every low cost/free brokerage allows trading it. It means you can transfer your brokerage holdings as many times as you want. Almost every brokerage runs new customer transfer bonuses. You can move your holdings yearly to a different brokerage and be paid $1+k/yr in doing so. $1k+ for 15 mins of effort can't be beat.
Now to start some dinosaur instruction drawings for
@aufheben