gofstat function in fitdistplus: interpretation for discrete values

Question

I have fitted a poisson and a negative binomial distribution to my count data using fitdist()in fitdistplus.

I want to assess which is the better fit to my data set using the gofstat()function but I would like to check if my interpretation, that a negative binomial is a better fit, is correct.

fnb <- fitdist(GrpSz_15$n_ans, "nbinom")
fpn <- fitdist(GrpSz_15$n_ans, "pois")

gofstat(list(fnb, fpn), fitnames = c("nbinom", "pois"))

Chi-squared statistic:  31.18916 73.59646 
Degree of freedom of the Chi-squared distribution:  2 3 
Chi-squared p-value:  1.687951e-07 7.242443e-16 
   the p-value may be wrong with some theoretical counts < 5  
Chi-squared table:
     obscounts theo nbinom theo pois
<= 2        99   68.874052 58.085759
<= 3        28   29.652668 36.857060
<= 4        16   23.929827 31.043298
<= 7        13   35.975958 38.315366
> 7         12    9.567495  3.698518

Goodness-of-fit criteria
                                 nbinom     pois
Akaike's Information Criterion 713.3276 752.3945
Bayesian Information Criterion 719.5755 755.5185

I understand that a lower information criteria means that distribution is a better fit. So in this case nbinom is a better fit to the observed data than poisson?

But I don't know how to fully interpret the chisq tables. Is it simply the value that is closer to the observed is better? Or should I be looking at the p value as well? And how do I interpret that? That both are significantly different from my observed, and therefore neither are good fits to the observed data?