Fattmerchant, Gravity Payments, and Worldpay are all great options for brick and mortar, and offer online payments too. Paypal is also cheaper than Stripe for US businesses.
As always, it depends, and it's complex. I probably was too confident in my above answer.
Stripe is an aggregator, which means they collect all payments and distribute to their clientele. This is why merchant processors like Square and Stripe can often get their customers up and running more quickly. Lower underwriting requirements = less regulation on the merchant. The level of risk is higher so they have to charge higher rates to cover their losses of fraud.
Gravity Payments is an Independent Sales Organization (ISO) which means they underwrite each merchant and "approve" each merchant account with their backend processor. This equals less fraud and more flexible pricing.
We do offer integrations and also have an online product that can process ecomm transactions for developer usage.