The difference between an AAVE and Morpho on Base is that Morpho users tend to heavily borrow alt. tokens other than ETH and stables and then deposit more stables. Aave users usually deal with stables and ETH. This means that Morpho's main advantage on Base is in alternative tokens like cbETH, BTC, and weETH, and fighting an incentive war on stables and ETH may be wasteful. However, not all is lost because, if you twist the scenario, Morpho subtly counter positioners AAVE when it comes to these alt. tokens. In terms of cross selling, sequentially speaking when they first handle these alt. tokens, they tend to trade more of them then move into stable deposits. Therefore, the incentive might be to get these users to deposit or borrow more stables after they have borrowed or deposited these alt. tokens. It's trickier for AAVE to cross-sell these alternative tokens towards other tokens, which again confirms that fighting a war directly on stables and ETH is difficult. They should focus on cross-selling. (Likewise, incentivising for such tokens on Arb may not be very helpful, especially when fighting against the entrenched AAVE.)

Ofc the exception to this is that morpho can provide superior yields on Arb and I definitely think this will happen (ofc risk profile is different) Then the bet becomes if you believe that users are indifferent to these risks and would just churn from aave to morpho