Difference in plotting the Power spectrum using two methods

Hello, Ihave the pulse signal-a1 attached which was sampled by suing freq of 64Hz and duration of signal is 10 seconds(as length=640).I used the following two methods

%---Method1---%

a1=load('a1.mat');
a1=a1.a1;
fs=64;
x_fft=fft(a1); %fft of the signal
N=length(a1);
omega=fs*[(0:N/2) (-N/2+1:-1)]/N; %frequency axis(bins)
figure(1);
plot(omega(1:N/2),2*abs(x_fft(1:N/2))); %plot of one-sided spectrum

%----method2---%

Fs=64 ; % insert here your frequency sampling in Hz
L=length(a1); 
NFFT = 2^nextpow2(L);
Y  = fft(a1,NFFT)/L;
f = Fs/2*linspace(0,1,NFFT/2+1);
figure(2);
plot(f,2*abs(Y(1:NFFT/2+1))) 
title('Single-Sided Amplitude Spectrum of y(t)')
xlabel('Frequency (Hz)')
ylabel('|Y(f)|')

the plots are

But I don't understand the difference between the both.

can someone explain me the difference between the two.

thanks.