Much less effective. 370W panel will have Vmp much higher than 12 ~ 15V, more like 30V.
For PWM to be comparable to MPPT and occasionally more efficient, PV panel Vmp needs to be close to battery voltage. Over a range of temperature it likely won't be. PWM is good for low cost, small system. MPPT should be used for just about everything else.
You really need to think about the watts you are having to put back into your system, that's what matters. If PWM can fully satisfy your demand in any weather conditions that MPPT can, PWM is fine. Conceptually MPPT wins when it comes to watts out but it simply may not be necessary in a small system so cost is the determining factor there and probably favours PWM.
Just make sure it is a charge controller that actually performs MPPT, maximum power point tracking.
There are some with "MPPT" in the brand name, which don't perform the function.
Some vendors claim their product is, to get you to buy them, even though they are PWM.
MPPT costs more, weights, more, and has specs that allow PV panel voltage to be significantly higher than battery voltage. (occasionally, also allow lower than battery voltage.) So if it is cheap, small, light weight, and only allows 24V max input, it is PWM not MPPT
PWM is just fine for a small system with PV panel nominally same as battery.
You said "370W panel" so we didn't even ask what voltage, knowing it was higher than 12V.
If you connect one or more "12V" panels in parallel (12V panels have Vmp between about 13V and 19V), those would be fine with PWM.
If that 370W panel is nominally 24V, or nominally 36V (Vmp 30V or so, or 45V or so), then PWM would be appropriate for charging 24V or 36V batteries, respectively.
Here are charge controllers from a vendor many of us have purchased from (PV panels in particular):
hi, maybe i’m to late here but according to Victron specifications (MPPT vs PWM section) for a 12v batt and 12v panel configuration, the PWM have the advantage of to be able of to charge during hot days where the Panel Open Voltage can drop to 16v and because a MPPT start to work when the PV is 5v higher than the battery voltage, a PWM have here an advantage..
i know the loss of efficiency of PWM, but during the hot days the mine still working ..for one 12v panel for a 12v battery, MPPT become not so interesting!!
note: MPPT act as a buck/down converter (never boost) and need a higher voltage..