In your experience, when getting a HELOC for your primary residence or investment property, do you think I'd be more likely to get a higher appraisal from a local lender or an online lender?
depends on how they do the appraisal.
for HELOC most appraisals are "bench top" meaning, it's a digital value assessment through comps and MAYBE someone will drive by the place. This allows the bank to reduce costs of transaction but the appraisal will be very conservative which is also good for the bank.
an actual appraisal where someone comes and checks out the house may give you a higher assessed value, but the cost to do so maybe higher as well.
The type of appraisal matters far more than who does it. Though my guess is online banks only do bench top. also know that banks almost universally want heloc appraisals to be conservative due to the nature of the debt (revolving)