Comparing ln(y) =bX vs. OLS and other count data models

#1
My data is a balanced panel.
12 years X 600 ids/year X 12 months = 864,000 observations.

For about 150 of my 600 ids, at a certain point in this 12 year period a treatment is applied switching them to the "treated" or "on" state. A dummy variable AFTER indicates when this is true.

My outcome is a count, positive only and quite skewed, looks like a power law.

I'm interested in estimating the impact of treatment on outcome.

I've tried these 3 specifications in STATA and I dont seem to understand why they don't accord well with each other.

1. OLS ---> reg y AFTER i.id i.year, robust cluster(id)
2. Logged --> reg ln(y) AFTER i.id i.year, robust cluster(id)
3. Poisson ---> xtpoisson y AFTER i.year, fe vce(robust)
4. Negative Binomial ---> nbreg y AFTER i.id i.year, vce(robust)

Here i.id and i.year are fixed effects for id and year respectively.

Estimated coeffs are as follows:
1. OLS: 403922 (223946) *
2. Log : -0.664 (0.0252) ***
3. Poisson : -.0188 (0.019)

Sum stats for my outcome variable are:

range: [0,3.025e+08] unique values: 59191

mean: 1.3e+06
std. dev: 1.1e+07

percentiles: 10% 25% 50% 75% 90%
0 13480 74690 322982 1.3e+06