Charging smallish 12V SLA requires that a charger meet two independent requirements:
1. to prevent damage to the battery if the charger is left on indefinitely, the charger output voltage must be limited to ~13.8V. In fancy three-state, microprocessor-controlled chargers, the charging voltage may go as high as 14.7V for several hours, but it will revert back to ~13.8V when the charger finally switches to "float" or "maintain" mode.
2. the initial charging current (when charging a mostly discharged battery) must be limited to a value less < = specified by the battery manufacturer (might be 1A for a 4AH battery, look it up). In inexpensive transformer-based chargers, the initial current limit is provided by core saturation in the transformer itself. In switchers, it is provided electronically.
If your new transformer-based wall-wart output current is different than the old one, it could be due to differences in the actual transformer used, how rectified (full vs half wave), internal filter capacitor or not, etc. Likely has nothing to do with the voltage limiter part.
To test any SLA charging system, just monitor charging current into the battery several hours after the battery voltage first reaches 13.8V. If after 24 to 48 hours, the battery is not sitting at ~13.8V with only a small leakage current (few mA) flowing into the battery, either the charger is junk or the battery is junk.