Is it better to use a MOSFET with a gate driver IC or a MOSFET with a lower VGS,on?
which is best for fast switching do I need to use MOSFET driver IC such as ICL766 with IRFZ44n or is it better to use lower VGS MOSFET such as AO3400
You don't want fast switching to drive LED strips! If the FET switches in a couple tens of nanoseconds, you will send very high di/dt currents into your wires which will radiate electromagnetic interference and essentially act like a broadband radio jammer. Remember a signal with 10ns edges has bandwidth extending to hundreds of MHz...
On the contrary, you want slow edges, like 0.5µs - 1µs. This increases switching losses, but your PWM frequency is going to be low anyway, so switching losses, which are proportional to frequency, will be low too. Let's check the math:
Conduction losses = RdsON * I^2 * DutyCycle
For 2 amps and a duty cycle of 1 (100%) a FET with RdsON of 40 mOhms dissipates 0.16W -- you can use a FET with lower RdsON if you want.
Switching losses = V * I * SwitchingTime * Frequency
For 12V, 2A, 500ns, 10kHz losses will be 0.12W.
Note these losses are already a bit high for a SOT23 FET. I'd use a SO8 single or dual FET instead, they have better dissipation and they're pretty cheap.
Say you want to switch an AO3400 in T=500ns, total gate charge is Qg=7nC so gate drive current will be roughly Qg/T = 14mA. For this you don't need a specialized gate drive IC.
If you have 5V available, you can use a 74HCT logic gate as voltage translator between your 3V3 micro and a 5V "logic level" MOSFET. It's cheap and it'll work.
If you only have 3V3 available and no 5V, and you don't want to bother with a separate 5V supply, then it makes sense to use a FET that is compatible with 3V3 drive. Depending on the gate drive current required, and the output drive capability of your micro, you might want to add a logic gate as a buffer too. 74LVC for example.
You cannot design ANY switch properly without specifying the load impedance R, C, L. tR and f rate.
Your switch RdsOn only needs to be < 1% of this load R for efficiency and cool operation with our large heatsink. But cost of FET may become a factor.
Vgs should be be 3x Vgsth for old std 2~4V thresold FETs or Vgs = 12V and only >2~2.5x for low Vth =1V FETs e.g. 3.3V. So your uC levels can consider these options for drivers if a boost is needed in Vgs. But remember that Coss increases as RdsOn decreases, which with cable L affects resonant frequency, so switch rise time, Q, and rep rate needs to be specified also.
For Visual RBW controls, you do not need a very fast rep rate compared to a 1MHz SMPS. Maybe 20kHz with PWM ??
When in doubt, datasheet specs for Vgs @ RdsOn ought to be observed for desired low loss and Coss & L cable to load R, ESR, or incremental R for resonance and series Q values. E.g. LED R ~= 0.5/P. Thus 100W = 5 milliohms , 1 W = 0.5 Ohm. And thus choose a switch that is near 1% of this for cool operation. More Ron demands attention to heat sink 1W/sq.in. of Cu area attached to SMD switch or as specified by datasheet.
For EMI reduction, consider a CM choke and X,Y cap as a PI filter to strip. This can be a Toroid or SMD choke. Use an AM radio to determine if you have EMI.
Bottom line: Compare Ron / R(LED) for loss ratio then decide on FET choices and then Vgs. The P rating of LEDs depends on array voltage and is irrelevant to this. Current and impedance ratio of switch is primary concern. Thus actual load tends to use only a small ratio of rated FET current at max heat sink rating.