Yes, both services have limits, especially for new accounts:
Stripe:
New accounts: $2,000 per week initially
Increases automatically based on processing history
Contact Stripe to request higher limits
After 3-6 months of consistent processing, most limits are removed
PayPal:
Unverified accounts: $500 receiving limit until verified
Verified accounts: $10,000 per transaction
$60,000 per transaction with sufficient history
Withdrawal limits: $1,000 per day initially, increases with account age